Relative excess probability (stacked image/random mean-1) for QSO (left) and galaxy (right) pairs considering the background sources within an angular radius of 200 arcsec from the position of the target. In both cases, the pixel size is 0.5 arcsec and we apply a 2.4σ Gaussian filter to take into account the positional uncertainties (see text for more details). The mean and standard deviation per pixel of the random stacked image for QSOs are 2.25 × 10⁻⁶ and 1.21 × 10⁻⁶, respectively, whereas the mean and standard deviation per pixel of the random stacked image for the galaxy sample are 2.32 × 10⁻⁶ and 1.15 × 10⁻⁶, respectively.